Plotting the Quadratic Function Using Parameters a, b and c

Here we have a quadratic equation.

A quadratic equation is always constructed like this:

$y = ax²+bx+c$

Where a, b, and c are generally already known to us, and the X and Y points need to be discovered.

Firstly, it seems that in this formula we do not have the C,

Therefore, we understand it is equal to 0.

$c = 0$

a is the coefficient of X², here it does not have a coefficient, therefore

$a = 1$

$b= 10$

is the number that comes before the X that is not squared.

To solve this problem, we'll clearly delineate the given expression and compare it to the standard quadratic form:

• Step 1: Recognize the standard form of a quadratic equation as $y = ax^2 + bx + c$.
• Step 2: Compare the given equation $y = x^2 - 6x + 4$ to the standard form.
• Step 3: Identify coefficients:
  - The coefficient of $x^2$ is $a = 1$.
  - The coefficient of $x$ is $b = -6$.
  - The constant term is $c = 4$.

Therefore, the coefficients for the quadratic function $y = x^2 - 6x + 4$ are $a = 1$, $b = -6$, and $c = 4$.

Among the provided choices, choice 3: $a=1,b=-6,c=4$ is the correct one.

To solve this problem, we'll follow these steps:

• Identify the given quadratic function.
• Match it with the standard form of a quadratic equation $y = ax^2 + bx + c$.
• Extract the values of $a$, $b$, and $c$ directly from the comparison.

Now, let's work through each step:
Step 1: The given quadratic function is $y = 2x^2 - 3x - 6$.
Step 2: The standard form of a quadratic equation is $y = ax^2 + bx + c$.
Step 3: By matching the given quadratic function with the standard form:

- The coefficient of $x^2$ is $2$, so $a = 2$.
- The coefficient of $x$ is $-3$, so $b = -3$.
- The constant term is $-6$, so $c = -6$.

Therefore, the solution to the problem is $a = 2$, $b = -3$, $c = -6$.

The quadratic equation of the given problem is already arranged (that is, all the terms are found on one side and the 0 on the other side), thus we approach the given problem as follows;

In the problem, the question was asked: what is the value of the coefficient$b$in the equation?

Let's remember the definitions of coefficients when solving a quadratic equation as well as the formula for the roots:

The rule says that the roots of an equation of the form

$ax^2+bx+c=0$are :

$x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

That is the coefficient$b$is the coefficient of the term in the first power -$x$We then examine the equation of the given problem:

$$$3x^2+8x-5 =0$That is, the number that multiplies

$x$ is

$8$Consequently we are able to identify b, which is the coefficient of the term in the first power, as the number$8$,

Thus the correct answer is option d.

Let's determine the coefficients for the quadratic function given by $y = -2x^2 + 3x + 10$.

• Step 1: Identify $a$.
  The coefficient of $x^2$ is $-2$. Thus, $a = -2$.
• Step 2: Identify $b$.
  The coefficient of $x$ is $3$. Thus, $b = 3$.
• Step 3: Identify $c$.
  The constant term is $10$. Thus, $c = 10$.

Comparing these coefficients to the provided choices, the correct answer is:

$a = -2, b = 3, c = 10$ .

Therefore, the correct choice is Choice 4.